Graph theory has become a powerful tool in the investigation of brain topological changes in diseased populations including AD ([1]}). While some previous studies use connectedness as a prerequisite condition to quantify other network attributes (e.g., shortest path length) ([2]}), they did not directly compare the connectedness. None of them has ever focused on more redundant network topology such as 2-connectedness. While a handful of previous works have investigated alternative paths ([3]}), none of them examined more stringent (2-)connected properties where all pairs of regions must have one (or more than one) independent paths. Our results suggested that these stringent global properties could be quite sensitive in tracking AD progression. We showed the first-ever evidence that time-varying brain connectedness can be informative to understand AD progression. While the majority of the complex brain network studies focused on the shortest pathsregions ([2]}) and the derived metrics (e.g., betweenness centrality ([5]}) and connector hub ([6]}), we showed that other lengthier pathways could be also informative, thanks to the similar concepts and applications in the other fields ([7]}, [8]}, [9]}, [10]}, [11]}). To further increase sensitivity, we extend such a concept to dynamic FC network by investigating how the brain changes its reserved paths in a time-varying manner, making it feasible to detect subtle changes in a diseased condition. The framework can be easily applied to other brain diseases and mental disorders.
